Mirka Miller's Combinatorics Webinar Series - Revision history

Mabreu at 22:52, 9 November 2026

2026-11-09T22:52:52Z

Mabreu: /* Upcoming Talks: */

2026-11-09T22:29:09Z

‎Upcoming Talks:

Mabreu at 22:27, 9 November 2026

2026-11-09T22:27:27Z

Mabreu at 14:29, 20 October 2026

2026-10-20T14:29:50Z

Mabreu: /* Upcoming Talks: */

2026-10-01T13:36:04Z

‎Upcoming Talks:

Mabreu at 13:34, 1 October 2026

2026-10-01T13:34:29Z

Cristina2: /* Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia) */

2026-09-17T12:43:01Z

‎Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia)

Cristina2: /* Previous Talks */

2026-09-17T12:41:55Z

‎Previous Talks

Cristina2: /* Upcoming Talks: */

2026-09-17T12:37:40Z

‎Upcoming Talks:

Mabreu: /* Upcoming Talks: */

2026-09-16T08:31:06Z

‎Upcoming Talks:

@@ Line 60: / Line 60: @@
 '''Video:'''
-'''Slides:''' [https://drive.google.com/file/d/1eKVRqY7Up3sb4bOS3yVL2ZJxpNBjFX6r/view?usp=drive_link https://drive.google.com/file/d/1eKVRqY7Up3sb4bOS3yVL2ZJxpNBjFX6r/view?usp=drive_link]
+'''Slides:''' [https://drive.google.com/file/d/1Najudu64Sj1aRxv9efLoAoJZYsIASImK/view?usp=sharing https://drive.google.com/file/d/1Najudu64Sj1aRxv9efLoAoJZYsIASImK/view?usp=sharing]
 ---

@@ Line 26: / Line 26: @@
 ''' Title: Hierarchy of Asymmetry of graphs'''
-'''Abstract: Although nearly all graphs are asymmetric, i.e. lack
+'''Abstract: ''' Although nearly all graphs are asymmetric, i.e. lack nontrivial global automorphisms, they are rich in non-trivial local symmetries, which can be studied through partial automorphisms (isomorphisms between induced subgraphs). In this talk, we explore the extent of graph asymmetry using the measure of asymmetric depth, defined by the rank of the largest non-trivial partial automorphism.
-Among other results, we present a general lower bound for the
+Among other results, we present a general lower bound for the asymmetric depth of any simple graph in terms of its order. We show that graphs achieving this bound must be conference graphs—strongly regular graphs with parameters (n, (n-1)/2, (n-5)/4, (n-1)/4)—which capture the "asymmetric spirit" of random graphs.
-To determine the tightness of this bound, we implemented a parallel
+To determine the tightness of this bound, we implemented a parallel (branch and bound) algorithm and ran it on high-performance-cluster to exhaustively check known asymmetric conference graphs. Our computational results identify asymmetric conference graphs on 37 vertices that attain the bound, proving its tightness and establishing 37 as the smallest possible order for such an extremal graph. We will also discuss related problems and future directions.
-This talk is based on joint work with Tatiana Jajcayová.'''
+This talk is based on joint work with Tatiana Jajcayová.

@@ Line 15: / Line 15: @@
 ==Upcoming Talks:==
-=== Giuseppe MAZZUOCCOLO (UniMoRe - Italy) - Disproving the Petersen Coloring Conjecture: Theoretical Analysis and an Infinite Family of Counterexamples ===
+=== Jan Pastorek (Comenius University, Bratislava, Slovakia) - Hierarchy of Asymmetry of graphs ===
 '''Date:''' October 21, 2026'''
@@ Line 23: / Line 63: @@
 '''Time''' 17:00 (CET)
-''' Speaker: Giuseppe MAZZUOCCOLO (Università di Modena e Reggio Emilia - Italy)'''
+''' Speaker: Giuseppe MAZZUOCCOLO (Università di Modena e Reggio Emilia - Italy) '''
 ''' Title: Disproving the Petersen Coloring Conjecture: Theoretical Analysis and an Infinite Family of Counterexamples'''
@@ Line 33: / Line 73: @@
 Join work with J. Goedgebeur, J. Jooken, E. Macajova, D. Mattiolo, N. Ulyanov
-[https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing]
+'''Video:'''
-Meet Link: [https://cuaed-unam-mx.zoom.us/j/84053189250 https://cuaed-unam-mx.zoom.us/j/84053189250] Meeting ID: 840 5318 9250
+'''Slides:''' [https://drive.google.com/file/d/1eKVRqY7Up3sb4bOS3yVL2ZJxpNBjFX6r/view?usp=drive_link https://drive.google.com/file/d/1eKVRqY7Up3sb4bOS3yVL2ZJxpNBjFX6r/view?usp=drive_link]
 ---
 ===Talk 55: Chordal graphs and generalizations - Mónica REYES===

@@ Line 35: / Line 35: @@
 [https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing]
-Meet Link: [https://meet.google.com/kgc-uwpc-ngp https://meet.google.com/kgc-uwpc-ngp]
+Meet Link: [https://cuaed-unam-mx.zoom.us/j/84053189250 https://cuaed-unam-mx.zoom.us/j/84053189250] Meeting ID: 840 5318 9250
 ----

← Older revision		Revision as of 13:36, 1 October 2026
Line 34:		Line 34:

	[https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing]		[https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing]
		+
		+	Meet Link: [https://meet.google.com/kgc-uwpc-ngp https://meet.google.com/kgc-uwpc-ngp]

	----		----

← Older revision		Revision as of 13:34, 1 October 2026
Line 15:		Line 15:
	==Upcoming Talks:==		==Upcoming Talks:==

		+	=== Giuseppe MAZZUOCCOLO (UniMoRe - Italy) - Disproving the Petersen Coloring Conjecture: Theoretical Analysis and an Infinite Family of Counterexamples ===



		+	'''Date:''' October 21, 2026'''
		+
		+	'''Time''' 17:00 (CET)
		+
		+	''' Speaker: Giuseppe MAZZUOCCOLO (Università di Modena e Reggio Emilia - Italy)'''
		+
		+	''' Title: Disproving the Petersen Coloring Conjecture: Theoretical Analysis and an Infinite Family of Counterexamples'''
		+
		+	'''Abstract: ''' In 1988, Jaeger conjectured that every bridgeless cubic graph G admits a Petersen coloring; that is, a map E(G) → E(P) mapping any two adjacent edges of G to two adjacent edges of the Petersen graph P. In this talk, we begin with a brief introduction to this problem and its deep implications for several famous, long-standing open problems in graph theory. We then recall recent breakthroughs, starting from July 2026, when a 68-vertex counterexample was announced on X, followed shortly by Putman’s two non-isomorphic 112-vertex counterexamples
		+	relying solely on computer-assisted verification. Mainly, we present two counterexamples of order 52, currently the smallest known, and provide the first purely theoretical proof explaining why they do not admit a Petersen coloring. Moreover, we show an infinite family of cyclically 4-edge-connected cubic graphs without a Petersen coloring for every even order at least 60. Additionally, through computational verification, we prove that any counterexample must have order at least 40. Finally, we show that our counterexamples provide a negative answer to other
		+	related problems.
		+
		+	Join work with J. Goedgebeur, J. Jooken, E. Macajova, D. Mattiolo, N. Ulyanov
		+
		+	[https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing https://drive.google.com/file/d/1LsRSu1igRFX9J6mJs5oGqU34nUDM5_zI/view?usp=sharing]

	----		----

@@ Line 25: / Line 25: @@
 ===Talk 55: Chordal graphs and generalizations - Mónica REYES===
@@ Line 52: / Line 50: @@
 ---
 ===Talk 54: Biregular Cages - György KISS===

← Older revision		Revision as of 12:41, 17 September 2026
Line 22:		Line 22:

	==Previous Talks==		==Previous Talks==
		+
		+	===Talk 55: Chordal graphs and generalizations - Mónica REYES===
		+
		+
		+	=== <big> '''Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia)'''</big> ===
		+
		+
		+	'''Date:''' September 16, 2026'''
		+
		+	'''Time''' 17:00 (CET)
		+
		+	''' Speaker: Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia) '''
		+
		+	''' Title: On Chordal Ring, Multi-ring and Mixed Graphs, and Three-Quarters Circulant Digraphs'''
		+
		+	'''Abstract: ''' Chordal ring graphs are a well-known family of graphs used to model interconnection networks. In this talk, we consider two families of graph and digraph structures related to circulant networks.
		+	First, we study chordal multi-ring, chordal ring mixed, and chordal multi-ring mixed graphs, which generalize the classical chordal ring graphs. Using plane tessellations, we obtain the maximum number of vertices for a given diameter. We also study these graphs as lift graphs over Abelian groups and obtain closed formulas for their spectra.
		+
		+	We then introduce a new family of three-quarters circulant digraphs associated with the cyclic group (\mathbb{Z}_N). Restricting the admissible combinations of two generators to three coordinate sectors gives a new distance-like function. The same geometric approach based on tessellations allows us to obtain Moore-type upper bounds for the order/diameter problem and construct infinite families with prescribed diameter. We give constructions for both even and odd diameters and discuss the maximum possible order.
		+
		+	Join work with Cristina Dalfó and Miquel Àngel Fiol
		+
		+	'''Video:''' [https://drive.google.com/file/d/1r8CL2X5RYdzUvbxxBoXxKVPpCPM2zEjD/view?usp=drive_link https://drive.google.com/file/d/1r8CL2X5RYdzUvbxxBoXxKVPpCPM2zEjD/view?usp=drive_link]
		+
		+	'''Slides:''' [https://drive.google.com/file/d/1eKVRqY7Up3sb4bOS3yVL2ZJxpNBjFX6r/view?usp=drive_link https://drive.google.com/file/d/1eKVRqY7Up3sb4bOS3yVL2ZJxpNBjFX6r/view?usp=drive_link]
		+
		+	'''Link:''' [https://teams.microsoft.com/l/meetup-join/19%3ameeting_NWM1ZTFhY2MtN2U1MS00ODg2LTgyZmItZTQwNmRmMTI4ODA2%40thread.v2/0?context=%7b%22Tid%22%3a%22fe8d7662-ab03-44d3-8787-fd718b76b5dd%22%2c%22Oid%22%3a%222b443e8c-3de6-43e0-87dc-970e1b830292%22%7d https://teams.microsoft.com/l/meetup-join/19%3ameeting_NWM1ZTFhY2MtN2U1MS00ODg2LTgyZmItZTQwNmRmMTI4ODA2%40thread.v2/0?context=%7b%22Tid%22%3a%22fe8d7662-ab03-44d3-8787-fd718b76b5dd%22%2c%22Oid%22%3a%222b443e8c-3de6-43e0-87dc-970e1b830292%22%7d]
		+
		+
		+	---
		+

← Older revision		Revision as of 12:37, 17 September 2026
Line 17:		Line 17:


−	~~=== <big> '''Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia)'''</big> ===~~
−
−
−
−
−	~~'''Date:''' September 16, 2026'''~~
−
−	~~'''Time''' 17:00 (CET)~~
−
−	~~''' Speaker: Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia) '''~~
−
−	~~''' Title: On Chordal Ring, Multi-ring and Mixed Graphs, and Three-Quarters Circulant Digraphs'''~~
−
−	'''Abstract: ''' Chordal ring graphs are a well-known family of graphs used to model interconnection networks. In this talk, we consider two families of graph and digraph structures related to circulant networks.
−	First, we study chordal multi-ring, chordal ring mixed, and chordal multi-ring mixed graphs, which generalize the classical chordal ring graphs. Using plane tessellations, we obtain the maximum number of vertices for a given diameter. We also study these graphs as lift graphs over Abelian groups and obtain closed formulas for their spectra.
−
−	We then introduce a new family of three-quarters circulant digraphs associated with the cyclic group (\mathbb{Z}_N). Restricting the admissible combinations of two generators to three coordinate sectors gives a new distance-like function. The same geometric approach based on tessellations allows us to obtain Moore-type upper bounds for the order/diameter problem and construct infinite families with prescribed diameter. We give constructions for both even and odd diameters and discuss the maximum possible order.
−
−	~~Join work with Cristina Dalfó and Miquel Àngel Fiol~~
−
−
−
−	'''Link:''' [https://teams.microsoft.com/l/meetup-join/19%3ameeting_NWM1ZTFhY2MtN2U1MS00ODg2LTgyZmItZTQwNmRmMTI4ODA2%40thread.v2/0?context=%7b%22Tid%22%3a%22fe8d7662-ab03-44d3-8787-fd718b76b5dd%22%2c%22Oid%22%3a%222b443e8c-3de6-43e0-87dc-970e1b830292%22%7d https://teams.microsoft.com/l/meetup-join/19%3ameeting_NWM1ZTFhY2MtN2U1MS00ODg2LTgyZmItZTQwNmRmMTI4ODA2%40thread.v2/0?context=%7b%22Tid%22%3a%22fe8d7662-ab03-44d3-8787-fd718b76b5dd%22%2c%22Oid%22%3a%222b443e8c-3de6-43e0-87dc-970e1b830292%22%7d]

@@ Line 24: / Line 24: @@
 '''Date:''' September 16, 2026'''
-'''Time''' 18:00 (CET)
+'''Time''' 17:00 (CET)
 ''' Speaker: Mónica A. Reyes (Universitat de Lleida, Igualada (Barcelona), Catalonia) '''