The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs

• Autorzy: Daniel W. Cranston , Sogol Jahanbekam , Douglas B. West
• Języki publikacji: EN

Abstrakty

EN

The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms the conjectures for graphs with maximum average degree less than 8/3. The conjectures are already confirmed for larger families, but the structure theorems and reducibility results are of independent interest.

Słowa kluczowe

EN

1; 2; 3-Conjecture; 1; 2-Conjecture; reducible configuration; discharging method.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 769-799

Daty

wydano

2014-11-01

otrzymano

2013-03-29

poprawiono

2013-11-13

zaakceptowano

2013-11-13

online

2014-11-15

Twórcy

autor

Daniel W. Cranston

• Virginia Commonwealth University Richmond, VA, USA

autor

Sogol Jahanbekam

• University of Colorado Denver Denver, CO, USA

autor

Douglas B. West

• Zhejiang Normal University, Jinhua, China and University of Illinois, Urbana, IL, USA

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1768